A240136 Prime numbers in the Antikythera mechanism.

19, 53, 127, 223

Offset: 1

Author

Michel Lagneau, Apr 02 2014

Keywords

• nonn
• fini
• full

Comments

The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the 2nd Century B.C. This device is a sophisticated arrangement of bronze gears, which can calculate the relative positions of the Sun and Moon, lunar phases and even eclipses. It is conjectured that it could also calculate the positions of the inner planets, but this is unproven. It was recovered from a Roman shipwreck in 1900 as a corroded mass of gear work. Detailed analysis could only really begin once X-ray equipment became available. Scans performed over the last 20 years have added significant clues as to the function and operation of the device. Ratios of gear tooth counts in the device indicate a good match to ratios used by the ancients to calculate the dates of eclipses using the Saros and Metonic cycles. Fragments of text recovered from the device mention the sun and moon and use month names used by the Greek city of Corinth and its colonies.

To understand the origin of these numbers, it is necessary to introduce other fundamental constants such as 365, 254, 235.

365: number of days in the Egyptian calendar. The X-ray scan of this zodiac fragment showed a ring of 365 holes.

Prime 19: number of years of the Meton cycle. The number 19 = 38/2 where 38 is the numbers of teeth in corresponding wheel of the mechanism. 19 years = 254 tropical months, and also 19 years = 235 synodic months.

235: Metonic constant or synodic months. There are 235 lunar months every 19 years that are arranged on a spiral.

Prime 223: 223 synodic months (or the Saros eclipse cycle), where 223 is the numbers of teeth counted in a wheel of the mechanism.

Prime 127 = Metonic cycle/2 = 254/2. The Moon appears to return to the same point in the sky relative to the zodiac in a sidereal month, and in 19 years there are 235 + 19 = 254 sidereal months. So, 127 is the numbers of teeth counted in a wheel of the mechanism.

Prime 53 = a gear-count which appears thrice in the device.

Remark: three primes 19, 53 and 223 are of the form 17*n+2 (A140544).

References

• Price, D. de S. Gears from the Greeks: The Antikythera Mechanism — A Calendar Computer from ca. 80 BC, Trans Am. Philos. Soc., New Series, 64, Part 7 (reprinted as Science History Publications, NY 1975), (1974)
• Wright, M.T. Epicyclic Gearing and the Antikythera Mechanism, Part I, Antiquarian Horology, Vol. 27 No. 3, pp. 270279, March (2003)
• Wright, M.T. Epicyclic Gearing and the Antikythera Mechanism, Part I, Antiquarian Horology, Vol. 27 No. 3, pp. 270279, March (2003)
• Wright, M.T. The Antikythera Mechanism and the Early History of the MoonPhase Display, Antiquarian Horology, Volume 29, No.3, March 2006, pp. 319329, (2006)
• Wright, M.T. Understanding the Antikythera Mechanism, Proceedings 2nd International Conferenceon Ancient Greek Technology, Technical Chamber of Greece, Athens, pp 4960, (2006)
• Freeth, T. The Antikythera Mechanism: 1. Challenging the Classic Research, Mediterranean Archaeology & Decoding the Antikythera Mechanism, published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). Archaeometry, Vol. 2 No. 1, pp. 2135, (2002)

Links

• Wikipedia, Antikythera mechanism